# Problem Specification – Lesson 1

### Learning Goals

In this tutorial, you will learn:

• Some of the fundamental aspects of particulate-laden flows.
• How to load a flow field initial condition from a file using a User Defined Function (UDF).
• How to use the Discrete Phase Model (DPM) to simulate particles in a flow.
• How to define particle injection using an injection file, and how to create injection files using MATLAB codes.
• How to visualize particle flow in CFD-Post.

### Problem Specification

In this tutorial, we study a case of particle-laden flows. The purpose is to illustrate some of the complex interactions between the fluid phase and a dispersed particle phase using commercially available tools. For this purpose, we study a 2D periodic double shear layer with disseminated particles as shown below:

Figure 1. Initial setup for the problem

A mixing layer occurs where two parallel streams flow at different velocities, resulting in a non-zero velocity gradient. In the absence of any perturbation, a mixing layer diffuses under the action of viscosity to the mean value of top and bottom velocities. However, in a real-life situation, the flow is subject to random perturbations, which causes it to destabilize and form vortices. The most potent perturbation can be computed using the Orr-Sommerfeld equation [1]. In this tutorial, we provide the Orr-Sommerfeld mode as an initial condition to the flow.

In the presence of particles, the vortices that result from the unstable perturbations offer interesting interactions with the suspended particles. In a general sense, "light" particles get trapped in the flow vortices, while "heavier" particles carrying more inertia might get expelled under a centrifugal type force from the swirling regions to gather along stretching regions of the flow [2,3]. This effect is known as preferential concentration and is illustrated in the following sketch:

Figure 2. Preferential concentration mechanism: particles gather along stretching regions and get expelled from vortical regions.

Formal definitions and a thorough discussion are provided in the Pre-Analysis section.